40 Mr. S. M. Drach on some new and curious 



The period of this planet's rotation being probably between 



3 1 



6^' and \2^. V — is between \'5 and 2'5, and the correspond- 

 q 



ing square is 'R 



5. As every body 'wif/iiti the limit must fall on the planet, 

 we may suppose the planetary sphere to extend to the limit, 

 and by Kepler's law, the rotation of a body at the limit of the 



Sun = 25''-78 Saturn's limit 8'''6472 



Earth = I'' -0086 Do. ring 13''-4 588 



Jupiter = lOh-OS^* Mean of do. 1].^652~ 



All of which are nearly coincident with the actual times of 

 rotation, and from these last the true value of q and ;• may 

 be found for every moon-attended planet. 



6. The greater the number of satellites, the more is the 

 danger that from some internal explosion or external shock a 

 moon might be precipitated upon the surface of its primary ; 

 hence the number of satellites must have influenced the rela- 

 tive or actual limit. The relative distance from the limit to 

 the surface of the star, is for the 



Sun =35-3942 Jupiter =1-319 



Earth = 5*619 Saturn =0-765. 



And our planet having one moon, Jupiter 4, and Saturn 7, 



1-319x4 = 5-276, 4" (0-765) = 1-338, 0-765 x 7 = 5-355, 

 4 



the results being nearly = the terrestrial and joval distances. 

 If this be correct, the sun must have 35-394-4- 5*619 = 6 to 

 7 satellites (primary planets) capable'of causing any se;70?/s da- 

 mage, which is the exact number of the large or older planets. 



7. If t denote the time, ;:; the height above a planet's sur- 

 face (radius =1), the equations of motion give 



^^ = -(rf^. +??('-=) = «»"-"• 



Whence -^ = ~^^ + . q (TT?'- 1) = g (3 5J -j). (3.) 



At the limit where q {\-\-zf = 1 ; g being the gravity in parts 

 of the radius, eq. (3.) expresses the velocity to send a body 

 up from the surface of the planet, or the velocity with which 

 a body let fall from the limit will impinge on the surface; 

 this is per second for the Sun 1,316,500 feet, Mercury 38,000 

 feet, Venus] 6960, Earth 17397, Mars 7858, Jupiter 144,080, 

 and Saturn 103,800 feet. 



8. The axis of the planet Venus being inclined at the sin- 

 gularly low angle of 15° to its orbit, its torrid zone extends 



